On a Smale problem

We derive conditions under which a linear coupling between two globally stable nonlinear n th-order systems results in a system of order 2 n whose almost every solution asymptotically approaches an orbitally stable cycle. These results permit one to solve a problem posed by Smale and pertaining to t...

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Bibliographic Details
Published in:	Differential equations Vol. 47; no. 1; pp. 1 - 9
Main Authors:	Burkin, I. M., Soboleva, D. V.
Format:	Journal Article
Language:	English
Published:	Dordrecht SP MAIK Nauka/Interperiodica 2011 Springer Nature B.V
Subjects:	Asymptotic methods Asymptotic properties Biological Chemical reactions Difference and Functional Equations Differential equations Eigenvalues Equilibrium Joining Kinetics Linear programming Mathematics Mathematics and Statistics Nonlinearity Ordinary Differential Equations Partial Differential Equations Reaction kinetics Studies Closed Trajectory Stable Cycle Complete Controllability Unique Equilibrium Global Oscillator
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Summary:	We derive conditions under which a linear coupling between two globally stable nonlinear n th-order systems results in a system of order 2 n whose almost every solution asymptotically approaches an orbitally stable cycle. These results permit one to solve a problem posed by Smale and pertaining to the theory of chemical kinetics of biological cells.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266111010010